Sorry, let me clarify. If your load balancer is on a droplet and your other servers are outside DO you would only use public IPs for everything. DO private IPs only allow for communication between two droplets in the same datacenter.

Since a load balancer simply routes traffic via HTTP/HTTPS it doesn't matter a lot what distro you use. If you're looking for consistency then, yes, it would make sense to go with the CentOS 6.x image we provide.